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| -rw-r--r-- | tables/resistor-aging-and-load-life-typical-magnitude.typ | 33 |
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diff --git a/module-design.typ b/module-design.typ index c295094..ca44492 100644 --- a/module-design.typ +++ b/module-design.typ @@ -2186,6 +2186,94 @@ $lt qty(0.2, "ppm per celsius")$ ($qty(200, "ppb per celsius")$). ===== Resistor aging and load life <resistor-aging-and-load-life> +====== Physical mechanism <resistor-aging-and-load-life-physical-mechanism> + +Resistors undergo long-term, irreversible baseline resistance changes over +operational lifetime due to four primary physical processes: + +/ Oxidation: Moisture and ambient oxygen slowly react with the resistive film or + foil element, altering effective conductive cross-sectional area. +/ Mechanical stress relaxation: Internal lattice strains induced during wire + drawing, foil rolling, or laser trimming gradually relax over time. +/ Electromigration: High DC current densities cause momentum transfer from + charge carriers to metal lattice ions, resulting in physical mass transport. +/ Moisture absorption: Protective epoxy or silicone encapsulants absorb ambient + moisture, altering dielectric properties and creating parasitic leakage + channels. + +These degradation mechanisms are thermally accelerated following Arrhenius +dynamics and exacerbated by power dissipation and ambient humidity cycling. + +====== Mathematical model <resistor-aging-and-load-life-mathematical-model> + +Unstressed shelf-life aging is modeled logarithmically over decades of +operational time: + +$ (Delta R)/R = A dot ln(t/t_0) $ + +Where: +- $A$ is the material aging coefficient ($unit("ppm per decade")$ of time). +- $t_0$ is the initial stabilization epoch (typically $qty(1000, "hour")$ + post-fabrication). + +Alternatively, for load-life aging under electrical power dissipation $P$: + +$ (Delta R)/R = B dot (P / P_0)^n dot sqrt(t/t_0) $ + +Where $P_0$ is nominal rated power, $0.5 lt.eq n lt.eq 1.0$ is the empirical +power exponent, and $B$ is the load-life stability factor. + +====== Typical magnitude <resistor-aging-and-load-life-typical-magnitude> + +#include "tables/resistor-aging-and-load-life-typical-magnitude.typ" + +For Metrologic tier ($qty(10, "ppm")$ total systemic budget), unpassivated +precision thin-film resistors ($qty(500, "ppm")$ per $qty(1000, "hour")$ load +life) consume the 30-day budget ($qty(10, "ppm")$) within the first +$qty(20, "hour")$ of continuous operation. + +Even ultra-stable bulk metal foil resistors ($qty(10, "ppm")$ per +$qty(1000, "hour")$ under full load) would consume the budget within +$qtyrange(1, 5, "year")$ without ratiometric cancellation or derating. + +====== Where it enters <resistor-aging-and-load-life-where-it-enters> + +/ Absolute reference scaling dividers: Resistors setting the + $+10.0000 upright("V")$ and $-10.0000 upright("V")$ system reference + standards. +/ Integrator time constants: Resistor drift in $tau = R C$ directly alters state + trajectory integration rates in time-domain compute cores. +/ Gain-determining feedback ratios: Unmatched discrete feedback resistors in + summing amplifiers and attenuators. + +====== Scaling law <resistor-aging-and-load-life-scaling-law> + +- Long-term baseline aging scales sub-linearly with time, following a + square-root ($sqrt(t)$) or logarithmic ($ln(t)$) relaxation trajectory. +- Power-induced aging scales with power density $(P / P_0)^n$ and accelerates + exponentially with operating junction temperature via Arrhenius thermal + acceleration ($exp(-E_a / (k_B T))$). +- In monolithic matched networks, aging mismatch between adjacent elements on + the same ceramic substrate scales at less than $qty(5, "percent")$ of absolute + single-element aging + ($Delta R_("aging","ratio") < 0.05 dot Delta R_("aging","abs")$), because + both elements share identical thermal, electrical, and metallurgical stress + histories. + +====== Compensation strategy <resistor-aging-and-load-life-compensation-strategy> + +/ Power derating: Operate precision resistors at $lt qty(10, "percent")$ of + their nominal rated power ($P lt.eq qty(10, "mW")$) to keep internal junction + self-heating below $qty(1, "celsius")$. +/ Pre-conditioning burn-in: Subject resistor networks to powered thermal + pre-aging ($qty(168, "hour")$ at $qty(125, "celsius")$) prior to initial + calibration to pass the steep initial logarithmic drift region. +/ Monolithic ratiometric design: Utilize integrated resistor networks where + aging tracking ($Delta R_("aging","ratio")$) governs circuit performance + rather than absolute drift. +/ Periodic reference recalibration: Recalibrate baseline offsets against the + system $plus.minus qty(10.0000, "V")$ reference standard. + == Error compensation strategies <error-compensation-strategies> == Advanced compensation topologies <advanced-compensation-topologies> diff --git a/tables/resistor-aging-and-load-life-typical-magnitude.typ b/tables/resistor-aging-and-load-life-typical-magnitude.typ new file mode 100644 index 0000000..c360f4d --- /dev/null +++ b/tables/resistor-aging-and-load-life-typical-magnitude.typ @@ -0,0 +1,33 @@ +// SAME Analog Modular Ecosystem +// +// / SPDX-FileCopyrightText: 2026 Denis Chevalier <perso@denischevalier.fr> +// / SPDX-License-Identifier: CC-BY-SA-4.0 +// / SPDX-License-Identifier: CERN-OHL-S-2.0+ +// / SPDX-License-Identifier: GPL-3.0-or-later +// +// The prose, explanatory text, rendered figures, tables, and mathematical +// content of this specification are licensed under CC BY-SA 4.0. If a later +// version of CC BY-SA is published, the author grants permission to distribute +// this work under that later version as well. +// +// Hardware designs contained herein (schematics, PCB layouts, mechanical +// drawings, and CAD models) are licensed under CERN-OHL-S-2.0+. +// +// All executable code, helper libraries (`lib/*`), metrology assertions, and +// embedded verification scripts throughout the source documents are licensed +// under the GNU General Public License v3.0 or later (GPL-3.0-or-later). + +#import "../lib/unify.typ": qty, qtyrange + +#figure( + table( + columns: 3, + table.header([Resistor type], [Aging rate], [Notes]), + [Carbon film], [$qty(500, "ppm per year")$], [At rated power], + [Metal film], [$qtyrange(50, 100, "ppm per year")$], [At rated power], + [Thin film], [$qtyrange(20, 50, "ppm per year")$], [At $qty(10, "percent")$ rated power], + + [Bulk metal foil], [$qtyrange(2, 10, "ppm per year")$], [At $qty(10, "percent")$ rated power], + ), + caption: [Resistor aging and load life typical magnitudes], +) <table-resistor-aging-and-load-life-typical-magnitude> |